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  {
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   "execution_count": 1,
   "id": "9f254bc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch.distributions import multinomial\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7c841735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair_probs = torch.ones([6]) / 6\n",
    "multinomial.Multinomial(1, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e663aee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2., 0., 2., 1., 1., 4.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomial.Multinomial(10, fair_probs).sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7b23aaa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1790, 0.1580, 0.1730, 0.1620, 0.1730, 0.1550])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 将结果存储为32位浮点数以进行除法\n",
    "counts = multinomial.Multinomial(1000, fair_probs).sample()\n",
    "counts / 1000  # 相对频率作为估计值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "33680064",
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   "outputs": [
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   "source": [
    "counts = multinomial.Multinomial(10, fair_probs).sample((500,))\n",
    "cum_counts = counts.cumsum(dim=0)\n",
    "estimates = cum_counts / cum_counts.sum(dim=1, keepdims=True)\n",
    "\n",
    "d2l.set_figsize((6, 4.5))\n",
    "for i in range(6):\n",
    "    d2l.plt.plot(estimates[:, i].numpy(),\n",
    "                 label=(\"P(die=\" + str(i + 1) + \")\"))\n",
    "d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
    "d2l.plt.gca().set_xlabel('Groups of experiments')\n",
    "d2l.plt.gca().set_ylabel('Estimated probability')\n",
    "d2l.plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31e22c37",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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